特殊平行四边形学习

特殊平行四边形学习
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2023-12-06 20:40
①本范例通过选择题和开放题演示特殊平行四边形(矩形、正方形、菱形、梯形)的识别与性质应用;②涉及核心概念:平行四边形、对角线、角度、边长关系;③构造摘要中用到了Point, Sequence, Translate, Polygon, Angle, Distance, Textfield, Segment, If, SpeechBubbleLeft, SelectedIndex, IndexOf, LaTeX等命令和对象进行图形绘制与交互;④适合小学高年级或初中一年级学生,用于几何概念理解和实践。

GeoGebra 命令及参数

  1. Point(Line[A2, xAxis]) → A3
  2. Sequence(A3 + (m * (0.2, 0)), m, 10, 25) → bpoints
  3. Translate(bpoints, Vector[(4 * UnitVector[v])]) → cpoints2
  4. Sequence(A4 + (m * (0.2, 0)), m, 10, 25) → bpoints4
  5. Point(bpoints) → B3
  6. Point(cpoints2) → C3
  7. Polygon(A3, B3, C3, D3) → v3, a3, b3, c3, d3
  8. Translate(bpoints4, (0.6, 4)) → cpoints4
  9. Point(cpoints4) → C4
  10. Point(bpoints4) → B4
  11. Sequence(A4 + ((m * 0.2), 4), m, -5, 3) → dpoints4
  12. Point(dpoints4) → D4
  13. Polygon(A4, B4, C4, D4) → v4, a4, b4, c4, d4
  14. Angle(v4) → σ, τ, υ, ϕ
  15. Sequence(A2 + ((m * 0.2), 4), m, -7, 3) → dpoints
  16. Point(dpoints) → D2
  17. Sequence(A2 + ((m * 0.2), 4), m, 23, 35) → cpoints
  18. Point(cpoints) → C2
  19. Polygon(A2, B2, C2, D2) → v2, l1_{2}, l1_{3}, l1_{4}, l1_{5}
  20. Angle(v2) → ι, κ, λ, μ
  21. Polygon(A5, B5, C5, D5) → v5, a5, b5, c5, d5
  22. Distance(D5, a5) → f
  23. Textfield(input5) → Eingabefeld5
  24. Textfield(input6) → Eingabefeld6
  25. Polygon(A, B, C, D) → v1, a, b, c, d
  26. Angle(v1) → α, β, γ, δ
  27. Sequence(FB0 + (m * (0, absfby)), m, 0, 4) → fbpoints
  28. Segment(A, B) → a2
  29. Segment(B, C) → b2
  30. Segment(C, D) → c2
  31. Segment(A, D) → d2
  32. Angle(v1) → ε, ζ, η, θ
  33. If(step ≤ 4, Element[{E1, E2, E3, E4}, step], If[step ≟ 7, E5, E4]) → E
  34. SpeechBubbleLeft(I1, 6.5, 1.1) → Vieleck1
  35. SpeechBubbleLeft(I2, 11.1, 1.1) → Vieleck2
  36. SpeechBubbleLeft(I3, 10.9, 0.7) → Vieleck3
  37. SpeechBubbleLeft(I4, 12.27, 1.05) → Vieleck4
  38. Distance(C1, Line[A1, B1]) → e
  39. SpeechBubbleLeft(I5, 10.3, 2) → Vieleck5
  40. SpeechBubbleLeft(I6, 10.2, 1.6) → Vieleck6
  41. SpeechBubbleLeft(I7, 10.2, 1.6) → Vieleck7
  42. Angle(v3) → ν, ξ, ο, ρ
  43. SpeechBubbleLeft(I8, 8, 1.1) → Vieleck8
  44. SpeechBubbleLeft(I9, 11.8, 1.6) → Vieleck9
  45. SpeechBubbleLeft(I10, 10.1, 1.9) → Vieleck10
  46. SelectedIndex(DropDown1) → input0
  47. SelectedIndex(DropDown2) → input00
  48. SpeechBubbleLeft(I11, 9.7, 0.6) → Vieleck11
  49. Polygon(A6b, B6, C6b, D6) → v6, v6_{2}, v6_{3}, v6_{4}, v6_{5}
  50. Polygon(A7b, B7b, C7b, D7b) → v7, a7b, b7b, c7b, d7b
  51. Polygon(A8b, B8b, C8b, D8) → v8, a8b, b8b, c8b, d8
  52. Angle(v6) → χ, ψ, ω, α_1
  53. Angle(v7) → β_1, γ_1, δ_1, ε_1
  54. Angle(v8) → ζ_1, η_1, θ_1, ι_1
  55. Angle(v5) → κ_1, λ_1, μ_1, ν_1
  56. If(step ≟ 2, 426, 510) → posBack
  57. IndexOf(C2, cpoints) → g
  58. LaTeX(g, true, true) → Text36
  59. If(κ / ° - floor(κ / °) < 0.5, floor(κ / °), ceil(κ / °)) → roundbeta1
  60. If(λ / ° - floor(λ / °) < 0.5, floor(λ / °), ceil(λ / °)) → roundgamma1
  61. If(μ / ° - floor(μ / °) < 0.5, floor(μ / °), ceil(μ / °)) → rounddelta1
  62. If(ι / ° - floor(ι / °) < 0.5, floor(ι / °), ceil(ι / °)) → roundalpha1
  63. If(σ / ° - floor(σ / °) < 0.5, floor(σ / °), ceil(σ / °)) → roundalpha2
  64. If(τ / ° - floor(τ / °) < 0.5, floor(τ / °), ceil(τ / °)) → roundbeta2
  65. If(υ / ° - floor(υ / °) < 0.5, floor(υ / °), ceil(υ / °)) → roundgamma2
  66. If(ϕ / ° - floor(ϕ / °) < 0.5, floor(ϕ / °), ceil(ϕ / °)) → rounddelta2

AI 绘图提示语参考

绘制一个平行四边形,然后依次绘制矩形、菱形、梯形。首先,通过点和线创建平行四边形的顶点,接着使用平移和序列命令生成其他形状的顶点。最后,通过角度和距离测量工具,验证每个形状的特性。
以上提示语为根据原始绘图命令整理而来,仅供参考。